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arXiv · 2502.14371

Asymptotic Existence of Class Envy-free Matchings

Tomohiko Yokoyama·Ayumi Igarashi
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Abstract

We consider a one-sided matching problem where agents who are partitioned into disjoint classes and each class must receive fair treatment in a desired matching. This model, proposed by Benabbou et al. [2019], aims to address various real-life scenarios, such as the allocation of public housing and medical resources across different ethnic, age, and other demographic groups. Our focus is on achieving class envy-free matchings, where each class receives a total utility at least as large as the maximum value of a matching they would achieve from the items matched to another class. While class envy-freeness for worst-case utilities is unattainable without leaving some valuable items unmatched, such extreme cases may rarely occur in practice. To analyze the existence of a class envy-free matching in practice, we study a distributional model where agents' utilities for items are drawn from a probability distribution. Our main result establishes the asymptotic existence of a desired matching, showing that a round-robin algorithm produces a class envy-free matching as the number of agents approaches infinity.

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Tomohiko Yokoyama, Ayumi Igarashi. 2025-02-20. Asymptotic Existence of Class Envy-free Matchings. https://arxiv.org/abs/2502.14371

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